Question

The weights of cars passing over a bridge have a mean of 3,550 pounds andstandard deviation of 870 pounds. Assume that the weights of the cars passing ovEthe bridge are normally distributed. Use a calculator or online z-score calculator, tofind the approximate probability that the weight of a randomly-selected car passingover the bridge is more than 4,000 pounds.

Answer 1

The Solution:

Given:

$\begin{gathered} x=4000 \\ \\ \mu=3550 \\ \\ \sigma=870 \end{gathered}$

Applying the Z-statistic formula:

$Z=\frac{x-\mu}{\sigma}=\frac{4000-3550}{870}=0.51724$

From the Z-scores tables:

The approximate probability of having a car weight that is more than 4000 pounds is:

$P(x>4000)=0.30249$

Converting the above probability to percent, we have:

$0.30249\times100=30.249\approx30\text{\%}$

Therefore, the correct answer is [ option D ]